“I was at a lunch with Jacob very recently and he indicated he would like to be considered for the leadership when the time comes,” Professor Malloch, who is close to US president Donald Trump, told The Mail on Sunday.

“He did not mean now, but at some point in the future.”

But in an interview with The Sunday Times, he played down the idea that he was ready to put himself forward as a new leader.

“I think if I threw my hat in the ring, my hat would be thrown back at me pretty quickly,” he said.

However, the paper quoted a friend of the MP as saying: “Jacob is loyal to a fault and would never do anything to destabilise Theresa May.

“But should she stand aside ... he is starting to look at some of his more ambitious peers and wonder what they have got that he hasn’t”.

When HuffPost UK spoke to Rees-Mogg in July, he was somewhat cryptic about the calls to run for the Tory leadership, simply laughing: “I don’t think giving one’s sixth child an unusual name is qualification for being prime minister.”

The “MP for the 18th century” attracted rather a lot of attention earlier this year for naming his sixth child Sixtus Dominic Boniface Christopher, joining Alfred Wulfric Leyson Pius, Peter Theodore Alphege, Tom Wentworth Somerset Dunstan, Anselm Charles Fitzwilliam and Mary (yes, just Mary) as the latest member of the Rees-Mogg clan.

The claims come just days after Rees-Mogg emerged as the second most popular choice to succeed Theresa May in a poll of Conservative Party members by the ConservativeHome website.

The findings reflect a belief among some Tories that the “young fogey” MP could be a right-wing antidote to the popularity of Labour leader Jeremy Corbyn.

Speaking on LBC, Tory Baroness Patience Wheatcroft said: “If Jacob Rees-Mogg became party leader, the Tory party would be absolutely killed. It would be the end.”